In a small bowl, whisk together the Greek yogurt, grated cucumber, lemon juice, and fresh dill to create a creamy tzatziki sauce, then set aside in the refrigerator.
In a mixing bowl, combine the ground lamb with the dried oregano, garlic powder, sea salt, and black pepper, mixing gently until the spices are evenly distributed.
Divide the seasoned lamb into two equal-sized balls and preheat a large cast-iron or non-stick skillet over medium-high heat.
Place the lamb balls into the hot skillet and immediately top each with a corn tortilla.
Using a heavy spatula or a burger press, firmly smash the tortilla down onto the lamb until the meat is flattened into a thin layer that covers the entire surface of the tortilla.
Cook for 3 to 4 minutes without moving, allowing the lamb to develop a deep, golden-brown crust.
Flip the tacos carefully so the tortilla side is down and cook for an additional 30 to 60 seconds until the tortilla is lightly toasted and pliable.
Transfer the tacos to a plate and garnish with the prepared tzatziki, diced tomatoes, sliced red onion, and crumbled feta cheese before serving.